Journal of Mathematical Physics
Using methods analogous to those introduced by Gel’fand et al. [Representations of the rotation and Lorentz Groups and Their Applications (Pergamon, New York, 1963)] for the Lorentz group the matrix elements for the representations of the Lie algebra of the Euclidean group in three dimensions E(3) are explicitly derived. These results are then used to construct invariant equations with respect to this group and to show, in particular, that the nonrelativistic analog to the Dirac equation is not unique.
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Copyright 1987 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Journal of Mathematical Physics 28(12) and may be found at http://link.aip.org/link/doi/10.1063/1.527730.
Humi, M. (1987). Representations and Invariant Equations of E(3). Journal of Mathematical Physics, 28(12), 2807-2811. http://dx.doi.org/10.1063/1.527730